1. Colin Folsom (Armagh Observatory)

2.  Read input  Calculate line components (Zeeman splitting)  Calculate continuum opacity (per window, per atmospheric layer)  Calculate line to continuum ratio (window, layer, line)  Calculate spectrum from each stellar surface element...

3.  For each: rotation phase, window, surface element  Determine local field  Determine strengths of components for each line  Calculate spectrum...

4.  For each: phase, window, surface element, layer  For each component of each line:  Calculate Voight profile, at each point in wavelength, with polarization information (Humlicek, 1982 algorithm)  For each point in wavelength, perform radiative transfer, for 4 Stokes parameters (Martin & Wickramasinghe, 1979; Landstreet,1988; Wade et al., 2001)

5.  Integration propagates through atmospheric layers  Surface elements are Doppler shifted and added  Gaussian instrumental profile applied  Windows and phases output separately

6.  Major time saving  Input and output compatible with magnetic  As similar routines as possible

7.  Assume horizontal homogeneity  Only need a line of surface elements rather then a disk (allows for correct v sin i and limb darkening)  Computation goes as v sin i rather then v sin i 2

8.  Skip separate Voight profiles for different components (save a factor of a few)  Voight profiles of one line at one layer are the same for all surface elements (only angle of emergent flux differs)  Go from proportional to v sin i to independent (save a factor of a few up to > 10)

9.  Don’t need: line components, local field, component strengths. (but save almost no time)  Can use non-polarized radiative transfer (relatively small time saving)

10.  Itot 10: 10 surface elements vs 100 1 Voight profile vs. a few 100 (per line, layer, window and phase)  133 lines (60 Å) in 5 sec vs. 849 sec  Identical non-magnetic results, down to machine precision.

11.  Zeeman acts as the fitting function  Preserve compatibility with regular Zeeman (easy upgrades)  Determine v sin i, microturbluence, abundances  Possibly T and logg...

12.  Use Levenberg Marquardt fitting algorithm:  Fast  Many parameters  Somewhat non-linear  Still can get stuck in local minima

13.  Conditions: 120 lines, 100 Å, 8 free parameters (vsini, microturbulence, Ca, Ti, V, Cr, Fe, Ba)  4 iterations, 41 Zeeman calls v sin i 10.9 km/s ξ 2.3 km/s Ca-6.13 Ti-6.98 V-7.68 Cr-6.19 Fe-4.55 Ba-9.44

15.  Repeat this process for several windows  Averages  Standard deviations  Discrepancies  Check result are sensible  Parameters are constrained  Inaccurate atomic data is not a (serious) problem

16.  Interpolating on a grid of model atmospheres  Constrain T by excitation potentials  And logg by ionization balance  Test results of throwing everything in  Calculate new abundance specific models, e.g. ATLAS12.

17. WindowT (K)Log g v sin i (km/s) ξ (km/s)FeTiCr 440091563.4810.72.2-4.564-7.094- 4500100804.1810.82.3-4.146-6.484-5.645 4600100054.2310.42.2-4.141-6.631-5.658 500094203.6710.52.6-4.407-6.959-5.971 520093633.5110.72.4-4.431-7.034-6.016 540092913.5210.42.7-4.464-7.184-6.011 Average95523.7710.582.40-4.36-6.90-5.86 Stdev3560.320.160.190.160.250.17 Luca's best fit93823.78101.9-4.3-6.86-6.01 uncertainty2000.20.50.20.070.040.07 HD 73666 comparison